Structural CDM. This draft: November, Pere Arqué-Castells 1 Universitat Autònoma de Barcelona & Institut d Economia de Barcelona

Transcription

1 Structural CDM This draft: November, 03 Pere Arqué-Castells Universat Autònoma de Barcelona & Instut d Economia de Barcelona Abstract In this paper we use the Crépon, Duguet and Mairesse (998) (hereafter, CDM) framework to model the subsidy-r&d-productivy link. We provide structure to each of the CDM equations to illustrate the precise way in which policy magnudes enter the continuous and discrete R&D equations and ultimately affect productivy. We estimate the structural CDM model and use to simulate the effects of variations in the subsidy policy on the intensive and extensive margins of R&D and on productivy. Keywords: Subsidies; R&D; Productivy; Dynamic models JEL Codes: H, O, C, D Tel.: ; fax: ; address: pere.arque@uab.cat

2 . Introduction R&D activies increase firms propensy to innovate which ultimately boosts firm-level productivy and aggregate welfare. Given the documented importance of R&D on productivy is of major interest for policymakers to learn how to use policy tools (such as R&D subsidies) to enhance productivy through R&D. Unfortunately, there is relatively ltle evidence on the link going from subsidies to productivy. The lerature gravating around the knowledge capal model (Griliches, 979) studies the effects of R&D on productivy, but totally overlooks the effects that policy actions have on R&D and productivy. Similarly, the lerature on R&D subsidies studies the effect of subsidies on R&D expendures, but is silent on whether these effects carry over to productivy. In this paper we set out to model the subsidy-r&d-productivy relationship thereby linking these two strands of the lerature that have remained incomprehensively isolated from one another so far. We regard the multi-equation model developed by Crépon, Duguet and Mairesse (998) (hereafter, CDM) as a promising starting point. The CDM model jointly specifies the different stages of the sequence going from the input choice to firm performance. The first stage describes the firm choice of innovation inputs and typically consists of an R&D selection equation and/or an R&D investment equation. The second stage links the firm s inputs of R&D to innovation outcomes by means of the so-called knowledge production function. The third relationship links innovation success to firm performance or productivy. Because the selection and continuous R&D equations are explicly taken into account, the CDM model has the potential for estimating how policy magnudes affect the R&D investment and participation decisions. Unfortunately, much of this promise gets blurred by the lack of structure originating the equations of the model. In other words, the equations of the CDM framework are not explicly derived from the firm s maximization problem. This makes

3 hard to tell how subsidies (or other policy magnudes) should enter the levels and selection R&D equations. In this paper we provide structure to each of the CDM equations so as to illustrate the precise way in which policy magnudes enter the continuous and discrete R&D equations and ultimately affect productivy. We first assume a knowledge accumulation process of the form proposed in Hall and Hayashi (989). We next derive productivy, continuous and discrete R&D equations consistent wh this process. The empirical productivy equation is derived according to the methodology outlined in Peters, Roberts, Vuong and Fryges (03) (hereafter, PRVF). Very stylized closed form continuous and discrete R&D equations are obtained from the optimaly condion derived in Klette and Johansen (996) and assuming R&D expendures (in logs) to follow a random walk. These three equations form the basis of what we refer to as a structural CDM (owing to the fact that every one of the parameters in the three equations of the CDM model contains information on structural parameters). Using data on Spanish manufacturing firms and following a sequential procedure we recover all the parameters of interest. In a first stage, we estimate the productivy equation and recover knowledge retention rates as well as the elasticy of productivy wh respect to R&D. In a second stage we estimate the R&D continuous equation (controlling for selection) and identify some addional parameters. In a third stage, wh the parameters identified in the productivy and the continuous R&D equations we estimate the selection equation. Finally, using the fully identified model we can simulate the effect of variations in subsidy shares on the number of R&D firms, total R&D investments and productivy evolution.

4 Roberts and Vuong (03) and PRVF also set out to overcome the weaknesses of the CDM model by developing a dynamic, structural model of the firm s demand for R&D. The main appeal of this structural approach is that allows changing parameters in the firm s environment (for instance the introduction of R&D subsidies) and quantifying how these changes affect the firm s decision to invest in R&D, s productivy, and the long-run impact on profabily. Therefore, the structural approach in PRVF provides a way to analyze the effects of policy decisions that affect the costs or benefs of R&D to the firms. There are two important differences between PRVF model and ours. The first one is that we assume a more specific process knowledge accumulation and derive a closed form analytical expression for the continuous R&D decision while they assume a more general process for productivy evolution and treat R&D as a discrete variable. Modeling the continuous R&D equation is important in our opinion because public subsidies are conceived as a share of to-be-made R&D expendures aimed at lowering the marginal cost of R&D investments. It is therefore not possible to simulate the effect of variations in R&D subsidies (as they exist in real world) unless the R&D investment equation is specified. The second one is that PRVF fully identify all the elements of the model while we treat the increment to the expected future value of the firm due to carrying out R&D as a residual. Since an important part of the effect of R&D subsidies on firms decision to carry out R&D operates through this term our model is thus far unable to successfully simulate the extensive margin effects of R&D subsidies.. Theoretical Model.. The firm s short-run profs The firm s short-run marginal cost function is given by c exp( ) K k W w 0 t exp( ) () 3

5 where c 0 is the marginal cost, K is the firm capal stock, variable inputs which every firm faces in period t and Wt is a vector of prices for captures differences in firm-specific technology or managerial abily. Each firm is assumed to produce one product, wh demand q t p exp( ) () where t are demand shifters in year t, p is the firm s output price, is the elasticy of demand wh respect to price and reflects product desirabily or qualy. The firm sets the price that maximizes s short-run prof: max ( p p c ) p exp( ) (3) t which yields the following first order condion p c (4) Given the FOC for price, the revenue function (i.e. sales) is ( ) exp( ) K k W w exp( ) S t 0 t (5) where. Following the related lerature we let 4

6 exp( ) G (6) wh G being the knowledge stock and the elasticy of productivy wh respect to knowledge. Profs are equal to S and can be wrten as ( G k w ( ) exp( ) K W G ) t 0 t A (7).. The knowledge accumulation process In what follows we will assume a knowledge accumulation process of the form proposed in Hall and Hayashi (989) and Klette (996). G R a0i 0 G exp (8) where R is the year t- R&D investment, is both the productiveness of R&D in generating new knowledge and the depreciation rate of previously acquired knowledge, a ~ N(, ) and ~ N(0, ). We are assuming constant returns to scale because 0i a0 a0 0 0 otherwise cannot be identified in the empirical application of the next section. As opposed to the perpetual inventory method, the knowledge accumulation process of equation (8) implies that old capal and new investment are complementary inputs in the production of 5

7 new knowledge. The basic idea is that greater inial knowledge will tend to increase the amount of knowledge obtained from a given amount of R&D (Klette, 996)..3. The firm s dynamic problem Firms choose their sequence of varible R&D expendures to maximize their value function (we could consider a more comprehensive scenario by acknowledging the importance of fixed and sunk R&D costs). V ( G ) ( G ) max EV ( G G, R 0) ( ) R ; EV ( G G, R 0) (9) where is the share of subsidized R&D expendures (i.e. we assume that subsidies decrease the marginal cost of R&D) and is the discount factor..3.. The continuous R&D decision R&D expendures can be eher posive or zero. The optimal posive investment is the one that maximizes the discounted sum of expected future profs net of the cost of R&D, or equivalently, that sets the marginal benef of an addional euro of R&D equal to the marginal cost. Formally, this amounts to solving the following Bellman equation subject to the knowledge accumulation process described by equation (8): V ( G R ) max ( G ) ( ) R EV ( G ) (0) 6

8 Notice that we take expectations because A and G are stochastic so their future realizations are unknown to the firm. The optimal R&D investment must satisfy the first order condion wh respect to R : V ( G ) G ( ) E 0 () G R and the envelope theorem V ( G E G ) ( G E G ) E V ( G G ) G G () Combining equations () and () we obtain ( G ( G ) G ) E E E[( )] E R G R G E G (3) Using equations (7), (8), (3) and rearranging we obtain ) ( ( ) R ( ) E[ A ]( R G ) ( ) E[( )] E[ R ] (4) This expression has no analytical solution for R. At this point we can eher resort to numerical methods (such as value function eration) or impose addional assumptions leading to closed form solutions. Since we want to stay as close as possible to the tradional 7

9 CDM framework (and derive analytical expressions for each of the three equations) we opt for the second alternative. One way in which we can obtain a closed form solution is by imposing the sixth stylized fact in Klette and Kortum (004) model of firm innovation, namely that firm R&D investment (in logs) follows a geometric random walk: R R R R exp( ) (i.e. E R ] R E[exp( )]) where ~ N(0, ) is iid. This R [ empirical regulary has been documented in Hall et al. (986) and Klette and Griliches (000) among others. R&D investments (in logs) also follow a random walk in every one of the industries in our database. Addionally, we assume that the marginal cost of R&D evolves as follows: ( ) ( ) exp( ) (i.e. E[( )] ( ) E[exp( )]) 0 where ~ N(0, ) is iid. Inserting the corresponding expressions for E [ R ] and E [( )] into equation (4) we obtain the following closed form solution for optimal R&D expendures: 0 R ( ) ( )( ) * E[ A ] G R (5) m ( ) where R and m ( ) ( ) E[exp( )exp( )] ( ) 0. In the Technical Appendix we show that the derived optimal R&D expendures in equation (5) follow a geometric random walk..3.. The discrete R&D decision The optimal R&D investment known, the firm chooses to invest in R&D if the expected future profs from doing R&D (net of the variable R&D cost) are greater than the expected future profs from not doing R&D: 8

10 EV G G, R 0) ( ) R EV ( G G, R 0) (6) ( noting that EV ( G G, R 0) E ( G G max EV ( G EV ( G, R 0) G G, R, R 0) ( 0) ) R ; (7) and defining EV max EV ( G EV ( G G G, R, R 0) ( ) R ; 0) EV ( G G, R 0) (8) we obtain E ( G R EV (9) G, R 0) ( ) Next, using E ( G ( ) a G, R 0) EA G EA R G exp 0i 0, plugging (5) into (9) and rearranging we obtain the following R&D selection equation ( R EV (0) ) * where m exp( a0i 0 ) E. This selection equation makes clear that as optimal R&D expendures increase so does the probabily that short run profs (gross of 9

11 variable R&D expendures) exceed the (minus) long run pay-off to investing in R&D (and therefore the probabily that firms engage in R&D). This nicely illustrates the posive relationship between the intensive and extensive margins of R&D observed in practice (the share of R&D firms of a given industry is always clearly posively correlated wh the average R&D expendure of active R&D firms in the same industry). 3. The three estimating equations of the CDM model 3.. Equation : The productivy equation Combining equations (6) and (8) and taking logs (we denote logs wh lower case letters in what follows) we obtain ( ) r a 0i 0 () where r ln( R ). This is the productivy equation that we would like to use as the third equation of the CDM model. The parameters of this equation contain important information on the elasticy of productivy wh respect to R&D ( ), the elasticy of productivy wh respect to knowledge stock ( ) and on how R&D effects manifest over time ( ). Of course, this equation is not estimable because productivy is not observable. In order to derive an estimable equation we follow PRVF who draw on the proxy variable approach pioneered by Olley and Pakes (996). Their insight is that if the firm observes s own productivy level before choosing s variable input levels then input demands are functions of productivy and the fixed factors of production, so information about productivy can be inferred from the expendure on variable inputs. Like PRVF we will also follow Levinsohn and Petrin (003) and focus on the choice of material spending. The firm s 0

12 demand for materials is m f k, ) where f t is assumed to be strictly monotone in t ( for a given k. Inverting the material demand function yields f t ( k, m ). Substuting into equation (5) and taking logs the revenue equation can be rewrten as: s D h( k, m ) u () 0 t t where u captures transory shocks in revenue, t Dt ( ) wwt ln t and h k, m ) ( ) k k 0 ( ) 0 ln, (. By approximating the term h k, m ) in a flexible way (e.g. a cubic function of s arguments) the revenue function can ( be estimated (separately for each industry) using OLS. Using the fted value ĥ from equation () and substuting hˆ k k into equation () we can recover the structural parameters of the productivy equation by estimating: h ˆ h ˆ k 3k 4r a i (3) where ( ), ˆ ( ) k, 3 ( ˆ)( ) k, ( ˆ ), a i ( ) a0i ˆ and ( ˆ ) 0. 4 In order to recover the structural parameters in equation (3) we need to know the elasticy of demand wh respect to price ˆ. We obtain this parameter by multiplying both sides of equation () by p and next regressing sales on an output price index (this yields estimates of

13 ˆ ). A common problem affecting sales or demand regressions like the one we estimate is that price is likely to be correlated wh the idiosyncratic error term given that firms are likely to react to posive (and unobserved) productivy shocks by increasing prices. This would clearly lead to an upward bias in the estimates of ˆ. In order to address this endogeney problem we instrument the output price index wh an intermediate materials price index and wh a dummy wh value one if firms state that price changes are due to variations in intermediate costs. Wh these two instruments we capture variation in prices caused by variations in intermediate materials costs (which should not be correlated wh omted factors affecting both price and sales). PRVF obtain the elasticy of demand from the expression for short-run prof (notice from equation (7) that S ). In particular, they use the mean prof-revenue ratio as an estimate of the inverse industry demand elasticy. Following this method we obtain disproportionately large values for the elasticy of demand (around -0). We believe that this is because our variable fort short-run prof considers some costs that are not strictly speaking variable costs. This is why we resort to sales regressions, which yield reasonable values for the elasticy of demand. 3.. Equation : The continuous R&D equation Taking logs of equation (5), approximating the expectation as a function of year t- realizations of s components plus an error term we obtain the following empirical continuous R&D equation (the algebra is shown in the Appendix): r * 0 g ln( m ( )) k a (4) 3 t i

14 where 0 ln ˆ ( ˆ) ln ˆ 0 ˆ, ( ˆ) ( ˆ)( ), ( ˆ), ( ˆ) ( ˆ) k 3, t ( ˆ) D t t ( ˆ), a and i ( ) ˆ i ( ˆ) Equation 3: The discrete R&D equation We use two discrete equations. The first one is simply used to control for selection when estimating (4) and is obtained by taking logs in both sides of (0) and inserting equation (4) into : y ln( ) 0 g ln( m ( ) ln( ) ) k 3 a t 3i 3 0 (5) where y is a dummy variable wh value one if the firm carries out R&D in t- and value zero otherwise, a a ln( EV ) and ln( EV ) (i.e., we have 3i i i 3 decomposed ln( EV ) into a time-invariant individual effect and an idiosyncratic error term). The second selection equation is obtained by taking logs in both sides of (0): * ln( ( ) R ) ln( EV ) (6) The elements of the right hand side of equation (6) known, is possible to estimate the mean and variance of ln( EV ) ~ N(, ) wh a prob regression. While this is ln( EV ) ln( EV ) valuable information that cannot be easily obtained whout a minimum structure (in standard prob regressions the variance is standardized at one and the mean is subsumed in the 3

15 constant of the model) is important to realize that EV is affected by changes in policy magnudes: increases in, and consequently in r, result in increases in EV or * reductions in ln( EV ). This implies that most of the extensive margin effects of subsidies on R&D will take place through EV, a term that we are treating as a residual so far. Therefore, in order to correctly assess the extensive margin effects of R&D subsidies we need to take into account how EV reacts to variations in the subsidy policy. PRVF do so by means of value function eration and this seems a natural (and almost mandatory) extension of our paper too. 4. Empirical strategy In order to identify the structural parameters of the three equations we carry out a sequential procedure. First, we estimate demand equations to estimate the elasticy of demand wh respect to price ˆ (see the Technical Appendix). Second, we estimate the revenue equation to calculate ĥ. Third, we estimate the productivy equation and identify the parameters, and the mean and variances of the error terms ( a 0 i and 0 ). Fourth, we estimate the parameters of the continuous R&D equation as well as the means and variances of the error terms ( a i and ). Fifth, we (re)estimate the discrete R&D equation and recover the mean and variance of ln( EV ). 5. Individual effects, selection and simultaney 5.. Individual effects 4

16 In order to deal wh the individual effects we will use the Wooldridge (005) approach to the inial condions problem. In other words, we will project in each equation the individual effects on the first observation of the corresponding lagged dependent variables: ˆ (7) a0i b00 b0r0i b0h0i b0i ˆ (8) a i b0 br0 i b h0i b i ˆ (9) a i b0 br0 i b h0i bi ˆ (30) a3i b30 b3r0 i b3 h0i b3i Where b 00, b 0, b 0 and b 30 are constants, dependent variables and b 0 i, b i, b i and r 0 i and hˆ 0 i are the inial values of the lagged b 3 i are i.i.d. normally distributed individual effects wh means zero and variances (where i 0,,, 3 ). Taking equations (7) to (30) into bi account, the final productivy and CDM equations look as follows: ˆ (3) b00 ( ) r b0r0 i b0h0i b0i 0 ˆ ˆ ˆ (3) h b0 h k 3k 4r b r0i b h0i b i r r ln( ) k b r b hˆ b (33) * 0 3 0i 0i i t y ln( ) ** 0 r k 3 ln( m b r 3 0i b ) ( ) ln( 3 hˆ 0i b 3i t ) 3 0 (34) ** * where 0 0 b0 and 0 0 b30 combine constants. It also projects in each equation the observed history of the other sufficiently time-varying explanatory variables. However, since our equations only have two explanatory variables (capal stock and subsidies), both wh ltle whin variation, we will om this term. 5

17 5.. Simultaney and selection We have assumed a one year gestation lag between R&D and productivy. An important implication of this timing assumption is that the idiosyncratic component of the productivy shock ( 0 ) enters contemporaneously in the idiosyncratic error term of the productivy equation but wh a lag in the continuous and discrete R&D equations (through g ). Given that is i.i.d. over time and across firms this implies that E [ ] 0. In words, we do 0 r 0 not need to worry about the potential simultaney of R&D when estimating the productivy equation (nor of selectivy given that the error terms of the productivy equation do not enter the error terms of the R&D equations). On the other hand, the error terms of the continuous and selection R&D equations share common elements so E[ ] 0. This implies that 3 is necessary to control for selection while estimating the continuous R&D equation. 6. Estimation method 6.. Equation : The productivy equation We estimate equation (3) using a maximum likelihood estimator for the standard linear regression model. We assume the individual effect to be normally distributed and integrate out using Gauss-Herme quadrature. Notice that alternative whin estimators such as difference or system GMM (Arellano-Bond, 99; Blundell and Bond, 998) are not well sued to identify the effects of R&D, a highly persistent variable. The random walk assumption implies that log differenced R&D is totally stochastic and cannot be instrumented for. This turns down difference (and to a lesser extent) system GMM as suable estimators. 6.. Equation : The continuous R&D equation 6

18 We estimate equation (4) controlling for selection wh equation (5). In order to deal wh selection and unobserved heterogeney we use Raymond et al. (00) maximum likelihood type- tob estimator. This estimator adapts the Wooldridge (005) approach to the inial condions problem originally conceptualized for a single equation to a multi-equations setting. The individual effects are assumed to follow a bivariate normal distribution and are integrated out using Gauss-Herme quadrature Equation 3: The discrete R&D equation Wh the variables in the RHS of (6) known to us ( is constructed using estimates of the productivy equation, ) is observed and ( * R is estimated as described in the previous stage) the mean and variance of ln( EV ) can be estimated wh a prob regression. 7. Data The dataset we use is the Encuesta Sobre Estrategias Empresariales (from now on ESEE). This survey gathers information from manufacturing firms operating in Spain employing more than nine workers. It is conducted on a yearly basis across twenty different sectors. The inial sampling undertaken in conducting the survey differentiated firms according to their size. While all firms employing more than 00 employees were required to participate, firms between 0 and 00 employees were selected by stratified sampling (stratification across the twenty sectors of activy and four size intervals). Subsequently, all newly created firms wh more than 00 employees together wh a randomly selected sample of firms between 0 and 00 employees have been gradually incorporated. The ESEE (Survey on Firm Strategies) has been conducted since 990 by the Fundación SEPI under the sponsorship of the Spanish Ministry of Industry. 7

19 The survey keeps track of the firms technological activy. We define R&D expendure as the sum of intramural expendure and, R&D contracted out wh external laboratories or research enties. In addion, the survey provides information on the public R&D funding received by R&D firms. This variable considers the total quanty of public aid granted by the various public agencies (primarily the national agency, CDTI, but also regional and European agencies). It must remain clear that this measure essentially includes subsidies but also other forms of public support such as low-interest and capal creds. We thus define the subsidy share as the sum of the total amount of public funding received by the firm over actual R&D expendures. The survey also provides information on firms capal stock and revenues. The dataset also includes an output price index that is used to deflate revenues and to estimate the elasticy of demand wh respect to price. Finally, we will use an intermediate materials price index and a dummy variable wh value one if the firm states that price changes are due to variations in intermediate costs as instruments for the output price index in the demand regression. We use information corresponding to the years 990 to 009 for ten industries. We retain observations observed for at least two periods (one for the inial condion and another for the lags in the R&D continuous and discrete equations). By now we will only show results corresponding to the industry on ferrous and non-ferrous metals and metal products which contains 3,469 observations and 464 firms. 8. Results Tables to 3 report the results of the productivy, continuous and discrete R&D equations. The most remarkable features of the productivy equation are that the elasticy of productivy wh respect to the knowledge stock is posive and significant and that the 8

20 depreciation rate is que low (below 0%). In the R&D equation we observe that R&D expendures depend posively on past knowledge stock. Finally, we estimate the selection equation separately for small (fewer than 00 employees) and large firms (more than 00 employees). The average value of ln( EV ) is larger for small firms. This means that the R&D premium (the increment to the expected value due to carrying out R&D today) is larger among large firms. Consequently, is easier for large firms to find profable to engage in R&D. 9. Simulations We simulate the effect of setting the subsidy share equal to 50% from the period 0 onwards. The corresponding figures show that this policy change causes a substantial increase in the average R&D expendures of active R&D firms, which swch from to (in logs). However, we can detect no effects neher on the share of R&D firms nor on average productivy. This is because we keep generating random draws of ln( EV ) based on the original estimates of the distribution of ln( EV ). However, this distribution is likely to change wh variations in the subsidy policy because increases in, and consequently in * r, result in increases in EV or reductions in ln( EV ). In other words, most of the extensive margin effects of subsidies on R&D are likely to take place through are ignoring this effect. EV and we 0. Conclusions In this paper we provide structure to each of the CDM equations so as to illustrate the precise way in which policy magnudes enter the continuous and discrete R&D equations and ultimately affect productivy. The estimated structural CDM model and subsequent 9

21 simulations reveal that while the continuous R&D equations behaves well, more structure needs to be added to the selection equation. Otherwise is not possible to quantify the long run benefs associated to (present) increases in R&D subsidies and extensive margin effects as well as productivy gains go unnoticed. References Arellano M, Bond S. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 99; 58; Blundell, R.W. and Bond, S.R. (998), Inial Condions and Moment Restrictions in Dynamic Panel Data Models, Journal of Econometrics, 87, Crèpon, B., Duguet, E. and Mairesse, J. (998), Research Innovation and Productivy: An Econometric Analysis at the Firm Level, Economics of Innovation and New Technology, Vol. 7, No., pp Griliches, Z. (979), Issues in assessing the contribution of R&D to productivy growth, Bell Journal of Economics 0(), 9 6. Hall, B.H., Griliches, Z. and Hausman, J.A. Patents and R and D: Is There a Lag?, International Economic Review 7 (June 986): Hall, B. & Hayashi, F. (989), Research and development as an investment, Working paper no. 973, NBER, Cambridge. 0

22 Klette, T.J. (996), R&D, scope economies, and plant performance, Rand Journal of Economics 7(3), Klette, T.J. and Griliches, Z. Empirical Patterns of Firm Growth and R&D-Investment: A Qualy Ladder Model Interpretation, Economic Journal 0 (April 000): Klette, T. and Johansen, F. (996), Accumulation of R&D Capal and Dynamic Firm Performance: A Not-so-fixed Effect Model, Discussion Papers No. 84 Statistics Norway, November 996. Klette, T.J. and Kortum, S. (004), "Innovating Firms and Aggregate Innovation, Journal of Polical Economy, (5), Levinsohn, J. and Petrin, A. (003), Estimating Production Function Using Inputs to Control for Unobservables, Review of Economic Studies, 70() (April), Olley, G.S. and Pakes, A. (996), The Dynamics of Productivy in the Telecomunications Eqipment Industry, Econometrica, 6(6) (November), Peters, B., Roberts, M., Vuong, V.A. and Fryges, H. (03), Firm R&D, Innovation, and Productivy in German Industries, mimeo. Raymond, W., Mohnen, P., Palm, F. and Schim van der Loeff, S. (00), Persistence of Innovation in Dutch Manufacturing: Is Spurious?, Review of Economics and Statistics, 9(3),

23 Roberts, M. and Vuong, V.A. (03), Empirical Modeling of R&D Demand in a Dynamic Framework, Applied Economic Perspectives and Policy, Vol.35 (), pp Wooldridge, J. (005), Simple Solutions to the Inial Condions Problem in Dynamic Nonlinear Panel Data Models wh Unobserved Heterogeney, Journal of Applied Econometrics, 0(), Variables definion R&D expendures. Cost of intramural R&D activies and R&D contracted wh external laboratories. R&D dummy variable. Dummy variable that takes the value one if R&D expendure is posive. Subsidy share. ratio of total public subsidies to total R&D expendure. Total R&D expendure of the firm includes the cost of intramural R&D activies and payments for outside R&D contracts (this definion of R&D is consistent wh the definion that is given in the Frascati Manual). Capal. Capal at current replacement values K ~ jt is computed recursively from an inial estimate and the data on current investments in equipment goods I ~ jt. We update the value of the past stock of capal by means of the price index of investment It jt jt P It as ~ ~ ~ K ( )( P P ) K I, where is an industry-specific estimate of the rate of jt It depreciation. Capal in real terms is obtained by deflating capal at current replacement ~ values by the price index of investment as K K P. jt jt jt Sales. total sales made by the firm, deflated by a firm-specific price index of output. Price of output. Firm-specific price index for output. Firms are asked about the price changes they made during the year in up to 5 separate markets in which they operate. The price index is computed as a Paasche-type index of the responses and and normalized by the average of s values for each firm. The firm-specific price index of output is calculated as follows. First, we assume that price levels are equal to one in 990 for all

24 firms. Next, we use a firm-specific output price change P / P that is provided by the ESEE to obtain a firm-specific output price level index for each period via the following recursive formula: P ( / ) P P P. If a firm is incorporated in the ESEE after 990 we assume that, from 990 to the year that the firm is incorporated, the firm s price index evolves according to the average price change observed in the industry the firm belongs to. Firm-specific price indexes have been calculated in a similar way in Mairesse and Jaumandreu (005) and Eslava et al. (004). Price of materials. Firm-specific price index for intermediate consumption. Firms are asked about the price changes that occurred during the year for raw materials, components, energy, and services. The price index is computed as a Paasche-type index of the responses and normalized by the average of s values for each firm. Price change due to intermediate costs: dummy variable wh value one if the firm states that price changes are due to variations in intermediate costs as instruments for the output price index in the demand regression. 3

25 Tables Table. Estimates of the productivy equation h t (0.09) *** k 0.39 (0.07) *** k t (0.07) *** r t (0.00) *** r (0.00) h (0.05) *** ct (0.073) *** 0.6 (0.004) *** b 0.0 (0.09) 0.08 (0.09) *** 0.06 (0.0) ** (0.46) *** # observations 3,469 Notes: ***, ** and * indicate significance at a %, 5% and 0% level respectively. The dependent variable is h Table. Estimates of the continuous R&D equation g t (0.03) *** k t (0.046) *** r (0.009) *** h (0.054) *** ct 3.40 (0.609) ***.49 (0.07) *** b (0.054) *** # observations,48 Notes: ***, ** and * indicate significance at a %, 5% and 0% level respectively. The dependent variable is r - 4

26 Table 3. Estimates of the discrete R&D equation ln( EV ) ln( EV ) ln( EV ) ln( EV ) Large firms (N=,006).89 (0.07) ***.394 (0.06) *** Small firms (N=,468) 3.03 (0.06) ***.497 (0.080) *** Notes: ***, ** and * indicate significance at a %, 5% and 0% level respectively. The dependent variable is r - 5

27 Figures ln(r&d expendures).5.5 Evolution of average R&D expendures for R&D firms Year Subsidy shares swch to 50% in year 0 Subsidy shares remain unchanged Evolution of R&D firms Share of R&D firms Year Subsidy shares swch to 50% in year 0 Subsidy shares remain unchanged 6

28 Evolution of average productivy Productivy (w) Year Subsidy shares swch to 50% in year 0 Subsidy shares remain unchanged 7